Statistical Models in R - University of Notre Dame

Statistical Models

Statistical Models in R

Some Examples Steven Buechler

Department of Mathematics 276B Hurley Hall; 1-6233

Fall, 2007

Statistical Models

Outline

Statistical Models Linear Models in R

Statistical Models

Regression

Regression analysis is the appropriate statistical method when the response variable and all explanatory variables are continuous. Here, we only discuss linear regression, the simplest and most common form.

Remember that a statistical model attempts to approximate the response variable Y as a mathematical function of the explanatory variables X1, . . . , Xn. This mathematical function may involve parameters. Regression analysis attempts to use sample data find the parameters that produce the best model

Statistical Models

Linear Models

The simplest such model is a linear model with a unique explanatory variable, which takes the following form.

y^ = a + bx.

Here, y is the response variable vector, x the explanatory variable, y^ is the vector of fitted values and a (intercept) and b (slope) are real numbers. Plotting y versus x, this model represents a line through the points. For a given index i, y^i = a + bxi approximates yi . Regression amounts to finding a and b that gives the best fit.

Statistical Models

Linear Model with 1 Explanatory Variable

10

5

y

q

q

q q

q

q

y qq q

q qq

q

q y-hat qq

q

q

q q

q

q

x=2

0

1

2

3

4

5

x

0

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download